(2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.5
|
|
- ちえこ とみもと
- 5 years ago
- Views:
Transcription
1 2007/5/14 II II x i x i 1 x i x i x i x x+dx f(x)dx f(x) f(x) + 0 f ( x) dx = 1 (Probability Density Funtion 2 ) (normal distribution) ( x m) / 2σ f ( x) = e 2πσ x m 2 N(m, 2 ) N(0,1) 1 2 PDF Adobe PDF 3 1
2 (2-1) x, m, 2 N(m, 2 ) x REAL*8 FUNCTION NRMDST (X, M, V) X,M,V REAL*8 x, m, 2 X X N(0,1) f(x) standard-norm.txt normdist1.f x=0, 0.31, 0.50, 1. 00, 2.00, N(0,1) , , , , normdist1.f FUNCTION =========================== Funtion NRMDST =========================== real*8 funtion nrmdst(x, m, v) =========================== Delaration of Arguments impliit none real*8 x, m, v =========================== Constants real*8 PI parameter (PI= d0) =========================== Funtion nrmdst = dexp (-(x - m)**2.0d0 / 2.0d0 / v) $ / $ dsqrt(2.0d0 * PI * v) end FUNCTION SUBROUTINE impliit none d0 REAL*8 56 PARAMETER PARAMETER( = ) x 5 REAL*8 FUNCTION SUBROUTINE 6 dble dble( ) 7 PARAMETER PARMATER(xdim=9, ydim=8, xydim=xdim*ydim) 8 DIMENSION PARAMETER C #define 2
3 SUBROUTINE. 11 Subroutine subroutine radiat $ ( I sun, solar, I dust, o2, O langwv, shrtwv $ ) I SUBROUTINE INPUT O SUBROUTINE FORTRAN v 2 dsqrt(2.0d0 * PI * v) (dsqrt(2.0d0 * PI) * dsqrt(v)) dsqrt dsqrt(2.0d0*pi) PARAMETER PI2SQR (PI2SQR * dsqrt(v)) 9 FORTRAN
4 (2-2) x N(0,1) f(x) REAL*8 FUNCTION STDNRM(x) ( x REAL*8 ) FUNCTION NRMDST impliit none real*8 x real*8 nrmdst stdnrm = nrmdst(x, 0.0d0, 1.0d0) ========================= x i x x a ( a x i a) x x a ( a x a) % a F(t) 12 F ( t) = f ( x) dx f(x) x 13 df( x) F(x) 0 0 lim F( x) = 0 lim F( x) = 1 dx x x m F(m+x)+F(m-x)=1, F(m)=0.5 (2-1) [a]n(0,1) 0.01 f(x) 0.00 x 4.00 x 0.01 F(x) erf1.txt PROGRAM ERF1( erf1.f) STDNRM 12 F(x) F(t) F(x) 13 y=f(x), y=x 4
5 program ERF1 Variables impliit none real*8 stdnrm real*8 x, minx, maxx, step real*8 nd, sum, prev integer i, ifirst, ilast Constants parameter (maxx=4.0d0, minx=0.01d0, step=0.01d0) Main Open File open(1, FILE='erf1.txt') Initialize ifirst = int(minx / step) ilast = int(maxx / step) sum = 0.5 prev = stdnrm(0.0d0) write first value (for x=0.0) write(6,1000)0.0, sum write(1,1000)0.0, sum Loop do i = ifirst, ilast x = dble(i) * step nd = stdnrm(x) sum = sum + $ ( step * ( nd + prev ) / 2 ) write(6, 1000)x, sum write(1, 1000)x, sum nd (f(x) ) --> prev prev = nd end do 1000 format(f6.2, F12.8) File Close lose(1) stop end 5
6 x (maxx, minx) (step) PARAMETER i maxx, minx, step f(x) f(x- x) f(x) prev FORMAT WRITE (2-3) erf1.txt N(0,1) F(1.0), F(2.0), F(3.0) F(x)=0.995 F(x)=0.975 x 14 ========= (2-4a) erf1.f erf2.f x<0-4 x 4 x 0.01 f(x), F(x) NDST, ERFA( ERFA(1)=F(0.01), ERFA(2)=F(0.02) ) x F(x) 2-1 nd-and-erf.dat (2-4b) N(0,1) f(x) F(x) 14 F(x)
7 erf2.f Initialize ifirst = int(minx / step) ilast = int(maxx / step) sum = 0.5 prev = stdnrm(0.0d0) Loop (for x>0) do i = ifirst, ilast x = dble(i) * step nd = stdnrm(x) sum = sum + $ ( step * ( nd + prev ) / 2 ) Store (tentative) results into arrays ndist(i) = nd erfa(i) = sum nd (f(x) ) --> prev prev = nd end do Calulation Finished Writing... Open File open(1, FILE='nd-and-erf.dat') (x:negative value) do i=ilast, ifirst, -1 x = - step * dble(i) write(6,1000)x, ndist(i), 1.0d0 - erfa(i) write(1,1000)x, ndist(i), 1.0d0 - erfa(i) end do (x:zero) x = 0.0d0 nd = stdnrm(x) write(6,1000)x, nd, 0.5 write(1,1000)x, nd, 0.5 (x:positive value) do i=ifirst, ilast x = step * dble(i) write(6,1000)x, ndist(i), erfa(i) write(1,1000)x, ndist(i), erfa(i) end do 1000 format(f6.2, 2F12.8) File Close lose(1) 7
8 F(x) x Hastings Hasting x 0 N(0,1) F(x) 1-0.5/w w=(a 0 + a x 1 + a 2 x 2 + a 3 x 3 + a 4 x 4 ) 4 a 0 =1.0, a 1 = , a 2 = , a 3 = , a 4 = x<0 F(x)=1-F( x ) 2-2 Hastings N(0,1) F(x) x FUNCTION ERFH4(x) ========================================================= Funtion ERFH4 N(0,1) F(x) Hastings 4 real*8 funtion erfh4(x) Delaration of Arguments and Funtions impliit none real*8 x, x1 real*8 w real*8 a0, a1, a2, a3, a4 parameter (a0 = 1.0, a1 = , $ a2 = , a3 = , a4 = ) Funtion x1 = dabs(x) w = a0 + a1 * x1 + a2 * x1 ** 2 + a3 * x1 ** 3 + a4 * x1 ** 4 w = w ** 4.0 if x >= 0 then erfh4 = / w else erfh4 = 0.5 / w end if end sign if ========================================================= Funtion ERFH4 N(0,1) F(x) Hastings 4 8
9 real*8 funtion erfh4(x) Delaration of Arguments and Funtions impliit none real*8 x real*8 w real*8 a0, a1, a2, a3, a4 parameter (a0 = 1.0, a1 = , $ a2 = , a3 = , a4 = ) Funtion w = a0 + x * (a1 + x * (a2 + x * (a3 + x * a4))) w = w ** 4.0 sign x erfh4 = sign( / w, x) end (2-5) 2.4 FUNCTION erfh4 x=-4.00,-3.99,,3.99,4.00 x, f(x), 2.4 F(x) Hastings F(x) nd-and-erf-hastings4.dat F(x) 9
10 2. X,Y Satter Diagram x (A vs B : r ) (A vs C : r (A vs D : r ) y i AvsB AvsC y i y i y i x i i y i y=ax+b x i y i y i y i y i (y i y i )=0 ( ) (y i y i ) 2 ( ) (y i y i ) 2 (ax i +by i y i ) 2 a b a b 0 a a = x y n x y ( x x)(y y) i i i i = 2 2 ) 2 x n x ( xi x i b y y = a( x x) x,y 10
11 2-6 INTEGER N,REAL*8 X(1000),Y(1000) R, A B SUBROUTINE REGRES N,X,Y,R,A,B orr.txt A B A B A D regres1.f 3. log y x x,y 11
12 15 proxy data 2-7 arib.dat orr.f A4 PDF DOC
Microsoft Word - 03-数値計算の基礎.docx
δx f x 0 + δ x n=0 a n = f ( n) ( x 0 ) n δx n f x x=0 sin x = x x3 3 + x5 5 x7 7 +... x ( ) = a n δ x n ( ) = sin x ak = (-mod(k,2))**(k/2) / fact_k 10 11 I = f x dx a ΔS = f ( x)h I = f a h I = h b (
More informationMicrosoft Word - 資料 (テイラー級数と数値積分).docx
δx δx n x=0 sin x = x x3 3 + x5 5 x7 7 +... x ak = (-mod(k,2))**(k/2) / fact_k ( ) = a n δ x n f x 0 + δ x a n = f ( n) ( x 0 ) n f ( x) = sin x n=0 58 I = b a ( ) f x dx ΔS = f ( x)h I = f a h h I = h
More information1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A B f : A B 4 (i) f (ii) f (iii) C 2 g, h: C A f g = f h g = h (iv) C 2 g, h: B C g f = h f g = h 4 (1) (i) (iii) (2) (iii) (i) (3) (ii) (iv) (4)
More information演習2
神戸市立工業高等専門学校電気工学科 / 電子工学科専門科目 数値解析 2017.6.2 演習 2 山浦剛 (tyamaura@riken.jp) 講義資料ページ h t t p://clim ate.aic s. riken. jp/m embers/yamaura/num erical_analysis. html 曲線の推定 N 次多項式ラグランジュ補間 y = p N x = σ N x x
More informationy = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f() + f() + f(3) + f(4) () *4
Simpson H4 BioS. Simpson 3 3 0 x. β α (β α)3 (x α)(x β)dx = () * * x * * ɛ δ y = x 4 y = x 8 3 y = x 4 y = x 3. 4 f(x) = x y = f(x) 4 x =,, 3, 4, 5 5 f(x) f() = f() = 3 f(3) = 3 4 f(4) = 4 *3 S S = f()
More informationjoho09.ppt
s M B e E s: (+ or -) M: B: (=2) e: E: ax 2 + bx + c = 0 y = ax 2 + bx + c x a, b y +/- [a, b] a, b y (a+b) / 2 1-2 1-3 x 1 A a, b y 1. 2. a, b 3. for Loop (b-a)/ 4. y=a*x*x + b*x + c 5. y==0.0 y (y2)
More information. (.8.). t + t m ü(t + t) + c u(t + t) + k u(t + t) = f(t + t) () m ü f. () c u k u t + t u Taylor t 3 u(t + t) = u(t) + t! u(t) + ( t)! = u(t) + t u(
3 8. (.8.)............................................................................................3.............................................4 Nermark β..........................................
More information1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1
1 21 10 5 1 E-mail: qliu@res.otaru-uc.ac.jp 1 1 ( ) ( 1.1 1.1.1 60% mm 100 100 60 60% 1.1.2 A B A B A 1 B 1.1.3 boy W ID 1 2 3 DI DII DIII OL OL 1.1.4 2 1.1.5 1.1.6 1.1.7 1.1.8 1.2 1.2.1 1. 2. 3 1.2.2
More informationFortran90/95 [9]! (1 ) " " 5 "Hello!"! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1
Fortran90/95 2.1 Fortran 2-1 Hello! 1 program example2_01! end program 2! first test program ( ) 3 implicit none! 4 5 write(*,*) "Hello!"! write Hello! 6 7 stop! 8 end program example2_01 1 program 1!
More information(Basic Theory of Information Processing) Fortran Fortan Fortan Fortan 1
(Basic Theory of Information Processing) Fortran Fortan Fortan Fortan 1 17 Fortran Formular Tranlator Lapack Fortran FORTRAN, FORTRAN66, FORTRAN77, FORTRAN90, FORTRAN95 17.1 A Z ( ) 0 9, _, =, +, -, *,
More information11042 計算機言語7回目 サポートページ:
11042 7 :https://goo.gl/678wgm November 27, 2017 10/2 1(print, ) 10/16 2(2, ) 10/23 (3 ) 10/31( ),11/6 (4 ) 11/13,, 1 (5 6 ) 11/20,, 2 (5 6 ) 11/27 (7 12/4 (9 ) 12/11 1 (10 ) 12/18 2 (10 ) 12/25 3 (11
More informationコンピュータ概論
4.1 For Check Point 1. For 2. 4.1.1 For (For) For = To Step (Next) 4.1.1 Next 4.1.1 4.1.2 1 i 10 For Next Cells(i,1) Cells(1, 1) Cells(2, 1) Cells(10, 1) 4.1.2 50 1. 2 1 10 3. 0 360 10 sin() 4.1.2 For
More informationall.dvi
fortran 1996 4 18 2007 6 11 2012 11 12 1 3 1.1..................................... 3 1.2.............................. 3 2 fortran I 5 2.1 write................................ 5 2.2.................................
More information18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
More informationii
ii iii 1 1 1.1..................................... 1 1.2................................... 3 1.3........................... 4 2 9 2.1.................................. 9 2.2...............................
More information1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 5 3. 4. 5. A0 (1) A, B A B f K K A ϕ 1, ϕ 2 f ϕ 1 = f ϕ 2 ϕ 1 = ϕ 2 (2) N A 1, A 2, A 3,... N A n X N n X N, A n N n=1 1 A1 d (d 2) A (, k A k = O), A O. f
More information9 8 7 (x-1.0)*(x-1.0) *(x-1.0) (a) f(a) (b) f(a) Figure 1: f(a) a =1.0 (1) a 1.0 f(1.0)
E-mail: takio-kurita@aist.go.jp 1 ( ) CPU ( ) 2 1. a f(a) =(a 1.0) 2 (1) a ( ) 1(a) f(a) a (1) a f(a) a =2(a 1.0) (2) 2 0 a f(a) a =2(a 1.0) = 0 (3) 1 9 8 7 (x-1.0)*(x-1.0) 6 4 2.0*(x-1.0) 6 2 5 4 0 3-2
More information³ÎΨÏÀ
2017 12 12 Makoto Nakashima 2017 12 12 1 / 22 2.1. C, D π- C, D. A 1, A 2 C A 1 A 2 C A 3, A 4 D A 1 A 2 D Makoto Nakashima 2017 12 12 2 / 22 . (,, L p - ). Makoto Nakashima 2017 12 12 3 / 22 . (,, L p
More informationii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.
24(2012) (1 C106) 4 11 (2 C206) 4 12 http://www.math.is.tohoku.ac.jp/~obata,.,,,.. 1. 2. 3. 4. 5. 6. 7.,,. 1., 2007 (). 2. P. G. Hoel, 1995. 3... 1... 2.,,. ii 3.,. 4. F. (),.. 5... 6.. 7.,,. 8.,. 1. (75%)
More information1 u t = au (finite difference) u t = au Von Neumann
1 u t = au 3 1.1 (finite difference)............................. 3 1.2 u t = au.................................. 3 1.3 Von Neumann............... 5 1.4 Von Neumann............... 6 1.5............................
More informationuntitled
Fortran90 ( ) 17 12 29 1 Fortran90 Fortran90 FORTRAN77 Fortran90 1 Fortran90 module 1.1 Windows Windows UNIX Cygwin (http://www.cygwin.com) C\: Install Cygwin f77 emacs latex ps2eps dvips Fortran90 Intel
More information() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
More information120802_MPI.ppt
CPU CPU CPU CPU CPU SMP Symmetric MultiProcessing CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU CP OpenMP MPI MPI CPU CPU CPU CPU CPU CPU CPU CPU CPU CPU MPI MPI+OpenMP CPU CPU CPU CPU CPU CPU CPU CP
More informationMicrosoft Word - 資料 docx
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 29 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 30 L A x y A L x 31 plot sine curve program sine implicit
More information1. A0 A B A0 A : A1,...,A5 B : B1,...,B
1. A0 A B A0 A : A1,...,A5 B : B1,...,B12 2. 3. 4. 5. A0 A, B Z Z m, n Z m n m, n A m, n B m=n (1) A, B (2) A B = A B = Z/ π : Z Z/ (3) A B Z/ (4) Z/ A, B (5) f : Z Z f(n) = n f = g π g : Z/ Z A, B (6)
More informationtokei01.dvi
2. :,,,. :.... Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN 4 3. (probability),, 1. : : n, α A, A a/n. :, p, p Apr. - Jul., 26FY Dept. of Mechanical Engineering, Saga Univ., JAPAN
More informationMicrosoft Word - 触ってみよう、Maximaに2.doc
i i e! ( x +1) 2 3 ( 2x + 3)! ( x + 1) 3 ( a + b) 5 2 2 2 2! 3! 5! 7 2 x! 3x! 1 = 0 ",! " >!!! # 2x + 4y = 30 "! x + y = 12 sin x lim x!0 x x n! # $ & 1 lim 1 + ('% " n 1 1 lim lim x!+0 x x"!0 x log x
More information01_OpenMP_osx.indd
OpenMP* / 1 1... 2 2... 3 3... 5 4... 7 5... 9 5.1... 9 5.2 OpenMP* API... 13 6... 17 7... 19 / 4 1 2 C/C++ OpenMP* 3 Fortran OpenMP* 4 PC 1 1 9.0 Linux* Windows* Xeon Itanium OS 1 2 2 WEB OS OS OS 1 OS
More information5 Armitage x 1,, x n y i = 10x i + 3 y i = log x i {x i } {y i } 1.2 n i i x ij i j y ij, z ij i j 2 1 y = a x + b ( cm) x ij (i j )
5 Armitage. x,, x n y i = 0x i + 3 y i = log x i x i y i.2 n i i x ij i j y ij, z ij i j 2 y = a x + b 2 2. ( cm) x ij (i j ) (i) x, x 2 σ 2 x,, σ 2 x,2 σ x,, σ x,2 t t x * (ii) (i) m y ij = x ij /00 y
More information情報処理概論(第二日目)
情報処理概論 工学部物質科学工学科応用化学コース機能物質化学クラス 第 8 回 2005 年 6 月 9 日 前回の演習の解答例 多項式の計算 ( 前半 ): program poly implicit none integer, parameter :: number = 5 real(8), dimension(0:number) :: a real(8) :: x, total integer
More information25 II :30 16:00 (1),. Do not open this problem booklet until the start of the examination is announced. (2) 3.. Answer the following 3 proble
25 II 25 2 6 13:30 16:00 (1),. Do not open this problem boolet until the start of the examination is announced. (2) 3.. Answer the following 3 problems. Use the designated answer sheet for each problem.
More information3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t + u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,., ν. t +
B: 2016 12 2, 9, 16, 2017 1 6 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : t = ν 2 u x 2, (1), c. t + c x = 0, (2). e-mail: iwayama@kobe-u.ac.jp,. 1 3. :, c, ν. 4. Burgers : t + c x = ν 2 u x 2, (3), ν. 5. : t +
More information, 1 ( f n (x))dx d dx ( f n (x)) 1 f n (x)dx d dx f n(x) lim f n (x) = [, 1] x f n (x) = n x x 1 f n (x) = x f n (x) = x 1 x n n f n(x) = [, 1] f n (x
1 1.1 4n 2 x, x 1 2n f n (x) = 4n 2 ( 1 x), 1 x 1 n 2n n, 1 x n n 1 1 f n (x)dx = 1, n = 1, 2,.. 1 lim 1 lim 1 f n (x)dx = 1 lim f n(x) = ( lim f n (x))dx = f n (x)dx 1 ( lim f n (x))dx d dx ( lim f d
More informationA B P (A B) = P (A)P (B) (3) A B A B P (B A) A B A B P (A B) = P (B A)P (A) (4) P (B A) = P (A B) P (A) (5) P (A B) P (B A) P (A B) A B P
1 1.1 (population) (sample) (event) (trial) Ω () 1 1 Ω 1.2 P 1. A A P (A) 0 1 0 P (A) 1 (1) 2. P 1 P 0 1 6 1 1 6 0 3. A B P (A B) = P (A) + P (B) (2) A B A B A 1 B 2 A B 1 2 1 2 1 1 2 2 3 1.3 A B P (A
More information08 p Boltzmann I P ( ) principle of equal probability P ( ) g ( )g ( 0 ) (4 89) (4 88) eq II 0 g ( 0 ) 0 eq Taylor eq (4 90) g P ( ) g ( ) g ( 0
08 p. 8 4 k B log g() S() k B : Boltzmann T T S k B g g heat bath, thermal reservoir... 4. I II II System I System II II I I 0 + 0 const. (4 85) g( 0 ) g ( )g ( ) g ( )g ( 0 ) (4 86) g ( )g ( 0 ) 0 (4
More informationnum3.dvi
kanenko@mbk.nifty.com http://kanenko.a.la9.jp/ ,, ( ) Taylor. ( 1) i )x 2i+1 sinx = (2i+1)! i=0 S=0.0D0 T=X; /* */ DO 100 I=1,N S=S+T /* */ T=-T*X*X/(I+I+2)/(I+I+3) /* */ 100 CONTINUE. S=S+(-1)**I*X**(2*i+1)/KAIJO(2*I+1).
More informationii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.
(1 C205) 4 10 (2 C206) 4 11 (2 B202) 4 12 25(2013) http://www.math.is.tohoku.ac.jp/~obata,.,,,..,,. 1. 2. 3. 4. 5. 6. 7. 8. 1., 2007 ( ).,. 2. P. G., 1995. 3. J. C., 1988. 1... 2.,,. ii 3.,. 4. F. ( ),..
More information3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2, (4), c. 2 u t 2 = c2 2 u x 2, (5) (1) (4), (1 Navier Stokes,.,
B:,, 2017 12 1, 8, 15, 22 1,.,,,,.,.,,,., 1,. 1. :, ν. 2. : u t = ν 2 u x 2, (1), c. u t + c u x = 0, (2), ( ). 1 3. :, c, ν. 4. Burgers : u t + c u x = ν 2 u x 2, (3), ν. 5. : u t + u u x = ν 2 u x 2,
More informationEvoltion of onentration by Eler method (Dirihlet) Evoltion of onentration by Eler method (Nemann).2 t n =.4n.2 t n =.4n : t n
5 t = = (, y, z) t (, y, z, t) t = κ (68) κ [, ] (, ) = ( ) A ( /2)2 ep, A =., t =.. (69) 4πκt 4κt = /2 (, t) = for ( =, ) (Dirihlet ondition) (7) = for ( =, ) (Nemann ondition) (7) (68) (, t) = ( ) (
More informationフローチャートの書き方
アルゴリズム ( 算法 ) 入門 1 プログラムの作成 機械工学専攻泉聡志 http://masudahp.web.fc2.com/flowchart/index.html 参照 1 何をどのように処理させたいのか どのようなデータを入力し どのような結果を出力させるのか問題を明確にする 2 問題の内容どおりに処理させるための手順を考える ( フローチャートの作成 )~アルゴリズム( 算法 ) の作成
More informationmain.dvi
1 F77 5 hmogi-2008f@kiban.civil.saitama-u.ac.jp 2013/5/13 1 2 f77... f77.exe f77.exe CDROM (CDROM D D: setupond E E: setupone 5 C:work\T66160\20130422>f77 menseki.f -o menseki f77(.exe) f77 f77(.exe) C:work\T66160\20130422>set
More information8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) Carathéodory 10.3 Fubini 1 Introduction 1 (1) (2) {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a
% 100% 1 Introduction 2 (100%) 2.1 2.2 2.3 3 (100%) 3.1 3.2 σ- 4 (100%) 4.1 4.2 5 (100%) 5.1 5.2 5.3 6 (100%) 7 (40%) 8 Fubini (90%) 2007.11.5 1 8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory
More informationOpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë
2012 5 24 scalar Open MP Hello World Do (omp do) (omp workshare) (shared, private) π (reduction) PU PU PU 2 16 OpenMP FORTRAN/C/C++ MPI OpenMP 1997 FORTRAN Ver. 1.0 API 1998 C/C++ Ver. 1.0 API 2000 FORTRAN
More information0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9
1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),
More informationOpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£±¡Ë
2011 5 26 scalar Open MP Hello World Do (omp do) (omp workshare) (shared, private) π (reduction) scalar magny-cours, 48 scalar scalar 1 % scp. ssh / authorized keys 133. 30. 112. 246 2 48 % ssh 133.30.112.246
More information- II
- II- - -.................................................................................................... 3.3.............................................. 4 6...........................................
More informationインテル(R) Visual Fortran Composer XE 2013 Windows版 入門ガイド
Visual Fortran Composer XE 2013 Windows* エクセルソフト株式会社 www.xlsoft.com Rev. 1.1 (2012/12/10) Copyright 1998-2013 XLsoft Corporation. All Rights Reserved. 1 / 53 ... 3... 4... 4... 5 Visual Studio... 9...
More informationr 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B
1 1.1 1 r 1 m A r/m i) t ii) m i) t Bt; m) Bt; m) = A 1 + r ) mt m ii) Bt; m) Bt; m) = A 1 + r ) mt m { = A 1 + r ) m } rt r m n = m r m n Bt; m) Aert e lim 1 + 1 n 1.1) n!1 n) e a 1, a 2, a 3,... {a n
More informationFortran90/95 2. (p 74) f g h x y z f x h x = f x + g x h y = f y + g y h z = f z + g z f x f y f y f h = f + g Fortran 1 3 a b c c(1) = a(1) + b(1) c(
Fortran90/95 4.1 1. n n = 5 x1,x2,x3,,x4,x5 5 average = ( x1 + x2 + x3 + x4 + x5 )/5.0 n n x (subscript) x 1 x 2 average = 1 n n x i i=1 Fortran ( ) x(1) x(2) x(n) Fortran ( ) average = sum(x(1:n))/real(n)
More information¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó
2 212 4 13 1 (4/6) : ruby 2 / 35 ( ) : gnuplot 3 / 35 ( ) 4 / 35 (summary statistics) : (mean) (median) (mode) : (range) (variance) (standard deviation) 5 / 35 (mean): x = 1 n (median): { xr+1 m, m = 2r
More informationx i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n
1, R f : R R,.,, b R < b, f(x) [, b] f(x)dx,, [, b] f(x) x ( ) ( 1 ). y y f(x) f(x)dx b x 1: f(x)dx, [, b] f(x) x ( ).,,,,,., f(x)dx,,,, f(x)dx. 1.1 Riemnn,, [, b] f(x) x., x 0 < x 1 < x 2 < < x n 1
More informationmugensho.dvi
1 1 f (t) lim t a f (t) = 0 f (t) t a 1.1 (1) lim(t 1) 2 = 0 t 1 (t 1) 2 t 1 (2) lim(t 1) 3 = 0 t 1 (t 1) 3 t 1 2 f (t), g(t) t a lim t a f (t) g(t) g(t) f (t) = o(g(t)) (t a) = 0 f (t) (t 1) 3 1.2 lim
More informationDVIOUT
A. A. A-- [ ] f(x) x = f 00 (x) f 0 () =0 f 00 () > 0= f(x) x = f 00 () < 0= f(x) x = A--2 [ ] f(x) D f 00 (x) > 0= y = f(x) f 00 (x) < 0= y = f(x) P (, f()) f 00 () =0 A--3 [ ] y = f(x) [, b] x = f (y)
More informationuntitled
I 9 MPI (II) 2012 6 14 .. MPI. 1-3 sum100.f90 4 istart=myrank*25+1 iend=(myrank+1)*25 0 1 2 3 mpi_recv 3 isum1 1 isum /tmp/120614/sum100_4.f90 program sum100_4 use mpi implicit none integer :: i,istart,iend,isum,isum1,ip
More information1 Introduction 1 (1) (2) (3) () {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a, b] lim f n (x) f(x) (1) f(x)? (2) () f(x)? b lim a f n (x)dx = b
1 Introduction 2 2.1 2.2 2.3 3 3.1 3.2 σ- 4 4.1 4.2 5 5.1 5.2 5.3 6 7 8. Fubini,,. 1 1 Introduction 1 (1) (2) (3) () {f n (x)} n=1 [a, b] K > 0 n, x f n (x) K < ( ) x [a, b] lim f n (x) f(x) (1) f(x)?
More information¥¤¥ó¥¿¡¼¥Í¥Ã¥È·×¬¤È¥Ç¡¼¥¿²òÀÏ Âè2²ó
2 2015 4 20 1 (4/13) : ruby 2 / 49 2 ( ) : gnuplot 3 / 49 1 1 2014 6 IIJ / 4 / 49 1 ( ) / 5 / 49 ( ) 6 / 49 (summary statistics) : (mean) (median) (mode) : (range) (variance) (standard deviation) 7 / 49
More informationMicrosoft Word - DF-Salford解説09.doc
Digital Fortran 解説 2009/April 1. プログラム形態とデ - タ構成 最小自乗法プログラム (testlsm.for) m 組の実験データ (x i,y i ) に最も近似する直線式 (y=ax+b) を最小自乗法で決定する 入力データは組数 mと m 組の (x i,y i ) 値 出力データは直線式の係数 a,bとなる 入力データ m=4 (x i,y i ) X=1.50
More information情報活用資料
y = Asin 2πt T t t = t i i 1 n+1 i i+1 Δt t t i = Δt i 1 ( ) y i = Asin 2πt i T 21 (x, y) t ( ) x = Asin 2πmt y = Asin( 2πnt + δ ) m, n δ (x, y) m, n 22 L A x y A L x 23 ls -l gnuplot gnuplot> plot "sine.dat"
More information6.1 (P (P (P (P (P (P (, P (, P.101
(008 0 3 7 ( ( ( 00 1 (P.3 1 1.1 (P.3.................. 1 1. (P.4............... 1 (P.15.1 (P.15................. (P.18............3 (P.17......... 3.4 (P................ 4 3 (P.7 4 3.1 ( P.7...........
More informationx () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
More information¥Ñ¥Ã¥±¡¼¥¸ Rhpc ¤Î¾õ¶·
Rhpc COM-ONE 2015 R 27 12 5 1 / 29 1 2 Rhpc 3 forign MPI 4 Windows 5 2 / 29 1 2 Rhpc 3 forign MPI 4 Windows 5 3 / 29 Rhpc, R HPC Rhpc, ( ), snow..., Rhpc worker call Rhpc lapply 4 / 29 1 2 Rhpc 3 forign
More information格子QCD実践入門
-- nakamura at riise.hiroshima-u.ac.jp or nakamura at an-pan.org 2013.6.26-27 1. vs. 2. (1) 3. QCD QCD QCD 4. (2) 5. QCD 2 QCD 1981 QCD Parisi, Stamatescu, Hasenfratz, etc 2 3 (Cut-Off) = +Cut-Off a p
More information1F90/kouhou_hf90.dvi
Fortran90 3 33 1 2 Fortran90 FORTRAN 1956 IBM IBM704 FORTRAN(FORmula TRANslation ) 1965 FORTRAN66 1978 FORTRAN77 1991 Fortran90 Fortran90 Fortran Fortran90 6 Fortran90 77 90 90 Fortran90 [ ] Fortran90
More informationOpenMP¤òÍѤ¤¤¿ÊÂÎó·×»»¡Ê£²¡Ë
2013 5 30 (schedule) (omp sections) (omp single, omp master) (barrier, critical, atomic) program pi i m p l i c i t none integer, parameter : : SP = kind ( 1. 0 ) integer, parameter : : DP = selected real
More information統計学のポイント整理
.. September 17, 2012 1 / 55 n! = n (n 1) (n 2) 1 0! = 1 10! = 10 9 8 1 = 3628800 n k np k np k = n! (n k)! (1) 5 3 5 P 3 = 5! = 5 4 3 = 60 (5 3)! n k n C k nc k = npk k! = n! k!(n k)! (2) 5 3 5C 3 = 5!
More information第13回:交差項を含む回帰・弾力性の推定
13 2018 7 27 1 / 31 1. 2. 2 / 31 y i = β 0 + β X x i + β Z z i + β XZ x i z i + u i, E(u i x i, z i ) = 0, E(u i u j x i, z i ) = 0 (i j), V(u i x i, z i ) = σ 2, i = 1, 2,, n x i z i 1 3 / 31 y i = β
More information2012 IA 8 I p.3, 2 p.19, 3 p.19, 4 p.22, 5 p.27, 6 p.27, 7 p
2012 IA 8 I 1 10 10 29 1. [0, 1] n x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 2. 1 x = 1 (n = 1, 2, 3,...) 2 f(x) = n 0 [0, 1] 1 0 f(x)dx 3. < b < c [, c] b [, c] 4. [, b] f(x) 1 f(x) 1 f(x) [, b] 5.
More information6.1 (P (P (P (P (P (P (, P (, P.
(011 30 7 0 ( ( 3 ( 010 1 (P.3 1 1.1 (P.4.................. 1 1. (P.4............... 1 (P.15.1 (P.16................. (P.0............3 (P.18 3.4 (P.3............... 4 3 (P.9 4 3.1 (P.30........... 4 3.
More information(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) (
B 4 4 4 52 4/ 9/ 3/3 6 9.. y = x 2 x x = (, ) (, ) S = 2 = 2 4 4 [, ] 4 4 4 ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, 4 4 4 4 4 k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) 2 2 + ( ) 3 2 + ( 4 4 4 4 4 4 4 4 4 ( (
More informationac b 0 r = r a 0 b 0 y 0 cy 0 ac b 0 f(, y) = a + by + cy ac b = 0 1 ac b = 0 z = f(, y) f(, y) 1 a, b, c 0 a 0 f(, y) = a ( ( + b ) ) a y ac b + a y
01 4 17 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy + r (, y) z = p + qy + r 1 y = + + 1 y = y = + 1 6 + + 1 ( = + 1 ) + 7 4 16 y y y + = O O O y = y
More informationOHP.dvi
0 7 4 0000 5.. 3. 4. 5. 0 0 00 Gauss PC 0 Gauss 3 Gauss Gauss 3 4 4 4 4 3 4 4 4 4 3 4 4 4 4 3 4 4 4 4 u [] u [3] u [4] u [4] P 0 = P 0 (),3,4 (,), (3,), (4,) 0,,,3,4 3 3 3 3 4 4 4 4 0 3 6 6 0 6 3 6 0 6
More informationa n a n ( ) (1) a m a n = a m+n (2) (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 552
3 3.0 a n a n ( ) () a m a n = a m+n () (a m ) n = a mn (3) (ab) n = a n b n (4) a m a n = a m n ( m > n ) m n 4 ( ) 55 3. (n ) a n n a n a n 3 4 = 8 8 3 ( 3) 4 = 8 3 8 ( ) ( ) 3 = 8 8 ( ) 3 n n 4 n n
More information1.2 y + P (x)y + Q(x)y = 0 (1) y 1 (x), y 2 (x) y 1 (x), y 2 (x) (1) y(x) c 1, c 2 y(x) = c 1 y 1 (x) + c 2 y 2 (x) 3 y 1 (x) y 1 (x) e R P (x)dx y 2
1 1.1 R(x) = 0 y + P (x)y + Q(x)y = R(x)...(1) y + P (x)y + Q(x)y = 0...(2) 1 2 u(x) v(x) c 1 u(x)+ c 2 v(x) = 0 c 1 = c 2 = 0 c 1 = c 2 = 0 2 0 2 u(x) v(x) u(x) u (x) W (u, v)(x) = v(x) v (x) 0 1 1.2
More informationI L01( Wed) : Time-stamp: Wed 07:38 JST hig e, ( ) L01 I(2017) 1 / 19
I L01(2017-09-20 Wed) : Time-stamp: 2017-09-20 Wed 07:38 JST hig e, http://hig3.net ( ) L01 I(2017) 1 / 19 ? 1? 2? ( ) L01 I(2017) 2 / 19 ?,,.,., 1..,. 1,2,.,.,. ( ) L01 I(2017) 3 / 19 ? I. M (3 ) II,
More information1 1 [1] ( 2,625 [2] ( 2, ( ) /
[] (,65 [] (,3 ( ) 67 84 76 7 8 6 7 65 68 7 75 73 68 7 73 7 7 59 67 68 65 75 56 6 58 /=45 /=45 6 65 63 3 4 3/=36 4/=8 66 7 68 7 7/=38 /=5 7 75 73 8 9 8/=364 9/=864 76 8 78 /=45 /=99 8 85 83 /=9 /= ( )
More information2 1,2, , 2 ( ) (1) (2) (3) (4) Cameron and Trivedi(1998) , (1987) (1982) Agresti(2003)
3 1 1 1 2 1 2 1,2,3 1 0 50 3000, 2 ( ) 1 3 1 0 4 3 (1) (2) (3) (4) 1 1 1 2 3 Cameron and Trivedi(1998) 4 1974, (1987) (1982) Agresti(2003) 3 (1)-(4) AAA, AA+,A (1) (2) (3) (4) (5) (1)-(5) 1 2 5 3 5 (DI)
More information( ) x y f(x, y) = ax
013 4 16 5 54 (03-5465-7040) nkiyono@mail.ecc.u-okyo.ac.jp hp://lecure.ecc.u-okyo.ac.jp/~nkiyono/inde.hml 1.. y f(, y) = a + by + cy + p + qy + r a, b, c 0 y b b 1 z = f(, y) z = a + by + cy z = p + qy
More information演習1
神戸市立工業高等専門学校電気工学科 / 電子工学科専門科目 数値解析 2019.5.10 演習 1 山浦剛 (tyamaura@riken.jp) 講義資料ページ http://r-ccs-climate.riken.jp/members/yamaura/numerical_analysis.html Fortran とは? Fortran(= FORmula TRANslation ) は 1950
More informationFgure : (a) precse but naccurate data. (b) accurate but mprecse data. [] Fg..(p.) Fgure : Accuracy vs Precson []p.0-0 () 05. m 0.35 m 05. ± 0.35m 05.
9 3 Error Analyss [] Danel C. Harrs, Quanttatve Chemcal Analyss, Chap.3-5. th Ed. 003. [] J. R. Taylor (, 000. An Introducton to Error Analyss, nd Ed. 997 Unv. Sc. Books) [3] 00 ( [] 973 Posson [5] 99
More informationMicrosoft Word - 信号処理3.doc
Junji OHTSUBO 2012 FFT FFT SN sin cos x v ψ(x,t) = f (x vt) (1.1) t=0 (1.1) ψ(x,t) = A 0 cos{k(x vt) + φ} = A 0 cos(kx ωt + φ) (1.2) A 0 v=ω/k φ ω k 1.3 (1.2) (1.2) (1.2) (1.1) 1.1 c c = a + ib, a = Re[c],
More information8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory 10.3 Fubini 1 Introduction [1],, [2],, [3],, [4],, [5],, [6],, [7],, [8],, [1, 2, 3] 1980
% 100% 1 Introduction 2 (100%) 2.1 2.2 2.3 3 (100%) 3.1 3.2 σ- 4 (100%) 4.1 4.2 5 (100%) 5.1 5.2 5.3 6 (100%) 7 (40%) 8 Fubini (90%) 2006.11.20 1 8.1 Fubini 8.2 Fubini 9 (0%) 10 (50%) 10.1 10.2 Carathéodory
More informationmain.dvi
3 4 2 3 4 2 3 ( ) ( ) 1 1.1 R n R n n Euclid R n R n f =(f 1 ;f 2 ;:::;f n ) T : f(x) =0 (1) x = (x 1 ;x 2 ;:::;x n ) T 2 R n 1 \T " f i (1 i n) R n R (1) f i (x) =0 (1 i n) n 2 n x =cosx f(x) :=x 0 cos
More informationD0050.PDF
Excel VBA 6 3 3 1 Excel BLOCKGAME.xls Excel 1 OK 2 StepA D B1 B4 C1 C2 StepA StepA Excel Workbook Open StepD BLOCKGAME.xls VBEditor ThisWorkbook 3 1 1 2 2 3 5 UserForm1 4 6 UsorForm2 StepB 3 StepC StepD
More information70の法則
70 70 1 / 27 70 1 2 3 4 5 6 2 / 27 70 70 70 X r % = 70 2 r r r 10 72 70 72 70 : 1, 2, 5, 7, 10, 14, 35, 70 72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 3 / 27 r = 10 70 r = 10 70 1 : X, X 10 = ( X + X
More informationAppendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1) (2) ( ) BASIC BAS
Appendix A BASIC BASIC Beginner s All-purpose Symbolic Instruction Code FORTRAN COBOL C JAVA PASCAL (NEC N88-BASIC Windows BASIC (1 (2 ( BASIC BASIC download TUTORIAL.PDF http://hp.vector.co.jp/authors/va008683/
More informationC言語によるアルゴリズムとデータ構造
Algorithms and Data Structures in C 4 algorithm List - /* */ #include List - int main(void) { int a, b, c; int max; /* */ Ÿ 3Ÿ 2Ÿ 3 printf(""); printf(""); printf(""); scanf("%d", &a); scanf("%d",
More informationAcrobat Distiller, Job 128
(2 ) 2 < > ( ) f x (x, y) 2x 3+y f y (x, y) x 2y +2 f(3, 2) f x (3, 2) 5 f y (3, 2) L y 2 z 5x 5 ` x 3 z y 2 2 2 < > (2 ) f(, 2) 7 f x (x, y) 2x y f x (, 2),f y (x, y) x +4y,f y (, 2) 7 z (x ) + 7(y 2)
More information.1 z = e x +xy y z y 1 1 x 0 1 z x y α β γ z = αx + βy + γ (.1) ax + by + cz = d (.1') a, b, c, d x-y-z (a, b, c). x-y-z 3 (0,
.1.1 Y K L Y = K 1 3 L 3 L K K (K + ) 1 1 3 L 3 K 3 L 3 K 0 (K + K) 1 3 L 3 K 1 3 L 3 lim K 0 K = L (K + K) 1 3 K 1 3 3 lim K 0 K = 1 3 K 3 L 3 z = f(x, y) x y z x-y-z.1 z = e x +xy y 3 x-y ( ) z 0 f(x,
More informationi
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
More informationB 90 Canvas.Pen.Width := PenWidth; NewData; (* FormCreate (*********************** ******************* procedure TFormSorting.DrawOne(No : TDat
B 89 14 14.1 14.1.1 SortingU SortingP 14.1.2 Form Name FormSorting Caption Position podesktopcenter 14.1.3 14.1.4 const NoMax = 400; DataMax = 600; PenWidth = 2; type TDataNo = 0..NoMax; TData = array
More informationsim98-8.dvi
8 12 12.1 12.2 @u @t = @2 u (1) @x 2 u(x; 0) = (x) u(0;t)=u(1;t)=0fort 0 1x, 1t N1x =1 x j = j1x, t n = n1t u(x j ;t n ) Uj n U n+1 j 1t 0 U n j =1t=(1x) 2 = U n j+1 0 2U n j + U n j01 (1x) 2 (2) U n+1
More informationN88 BASIC 0.3 C: My Documents 0.6: 0.3: (R) (G) : enterreturn : (F) BA- SIC.bas 0.8: (V) 0.9: 0.5:
BASIC 20 4 10 0 N88 Basic 1 0.0 N88 Basic..................................... 1 0.1............................................... 3 1 4 2 5 3 6 4 7 5 10 6 13 7 14 0 N88 Basic 0.0 N88 Basic 0.1: N88Basic
More information( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1
( )/2 http://www2.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html 1 2011 ( )/2 2 2011 4 1 2 1.1 1 2 1 2 3 4 5 1.1.1 sample space S S = {H, T } H T T H S = {(H, H), (H, T ), (T, H), (T, T )} (T, H) S
More informationbody.dvi
..1 f(x) n = 1 b n = 1 f f(x) cos nx dx, n =, 1,,... f(x) sin nx dx, n =1,, 3,... f(x) = + ( n cos nx + b n sin nx) n=1 1 1 5 1.1........................... 5 1.......................... 14 1.3...........................
More informationi 18 2H 2 + O 2 2H 2 + ( ) 3K
i 18 2H 2 + O 2 2H 2 + ( ) 3K ii 1 1 1.1.................................. 1 1.2........................................ 3 1.3......................................... 3 1.4....................................
More information[ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx A p.2/29
A p./29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx A p.2/29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx [ ] F(x) f(x) C F(x) + C f(x) A p.2/29 [ ] x f(x) F = f(x) F(x) f(x) f(x) f(x)dx [ ] F(x) f(x) C F(x)
More informationCALCULUS II (Hiroshi SUZUKI ) f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b)
CALCULUS II (Hiroshi SUZUKI ) 16 1 1 1.1 1.1 f(x, y) A(a, b) 1. P (x, y) A(a, b) A(a, b) f(x, y) c f(x, y) A(a, b) c f(x, y) c f(x, y) c (x a, y b) lim f(x, y) = lim f(x, y) = lim f(x, y) = c. x a, y b
More informationex01.dvi
,. 0. 0.0. C () /******************************* * $Id: ex_0_0.c,v.2 2006-04-0 3:37:00+09 naito Exp $ * * 0. 0.0 *******************************/ #include int main(int argc, char **argv) double
More informationPart () () Γ Part ,
Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
More information